DC motors worksheet with answers

Free printable DC motors worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
+−120 VRa​ = 0.5 ΩIa​ = 20 AM+−EωT

A DC motor runs from 120 V with an armature current of 20 A. The armature resistance is 0.5 Ω. Find the developed (electromagnetic) power Pdev.

V = 120 VIa = 20 ARa = 0.5 Ω
Pdev = W
2.Easy
+−110 VRa​M+−E = 98 Vn = 1450 rpmT

A DC motor turns at 1450 rpm, and its back-EMF at that speed is 98 V. Find the motor constant k in V·s/rad.

E = 98 Vn = 1450 rpm
k = V·s/rad
3.Medium
+−240 VRa​ = 0.5 ΩIa​ = 50 AM+−EωT

A DC motor draws 50 A from a 240 V supply. Its armature resistance is 0.5 Ω and its rotational (friction, windage and iron) losses are 860 W. Find its efficiency η.

V = 240 VIa = 50 ARa = 0.5 ΩProt = 860 W
η = %
4.Medium
+−110 VRa​ = 2 ΩIa​ = 4 AM+−EωT

A DC motor draws 4 A from a 110 V supply. Its armature resistance is 2 Ω and its rotational (friction, windage and iron) losses are 12 W. Find its efficiency η.

V = 110 VIa = 4 ARa = 2 ΩProt = 12 W
η = %
5.Hard
+−48 VRs​ = ?Ra​ = 1 ΩM+−En = 400 rpmT = 1.2 N·m

A DC motor (k = 0.6 V·s/rad, Ra = 1 Ω) on a fixed 48 V supply drives a load of 1.2 N·m. Find the series resistance Rs that slows it down to 400 rpm.

V = 48 Vk = 0.6 V·s/radRa = 1 ΩT = 1.2 N·mn = 400 rpm
Rs = Ω
6.Hard
+−24 VRa​ = 4 ΩM+−EωT

A small DC motor has an armature resistance of 4 Ω and runs from 24 V. Neglecting rotational losses, find the largest mechanical power Pmax it can develop at any speed.

V = 24 VRa = 4 Ω
Pmax = W

Answer key

  1. 1. Pdev = 2200 W
  2. 2. k = 0.6454 V·s/rad
  3. 3. η = 82.42 %
  4. 4. η = 90 %
  5. 5. Rs = 10.43 Ω
  6. 6. Pmax = 36 W

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